Type II topoisomerases are essential enzymes common to all organisms. Their cellular functions include maintaining the levels of chromosome compaction and ensuring proper segregation at cell division. In addition they are often used as targets for antimicrobial agents and anticancer drugs. Understanding the process by which topoisomerase II (topo II) simplifies the topological complexity of its DMA substrate is of key importance. By a cut-and-paste mechanism, which is well understood at the molecular level, topo II is able to pass a DMA segment through another. How topo II recognizes the two DMA segments is still unclear. Topo II is known to unknot and decatenate DMA to levels below those expected by random strand-passage. These and other experimental observations suggest a chirality-driven non-random mechanism of topo II action. Numerous experimental and theoretical studies have addressed these questions. However a clear picture of the mechanism of topo II is still lacking. Our long-term goal is to find an accurate model for the mechanism of topology simplification by topo II. We here focus on the process of DNA unknotting. Our objective is to verify whether topo II has the ability to unknot DMA in the smallest possible number of strand-passages, or whether a chirality bias combined with other local information are sufficient to reach the experimentally observed unknotting levels. We propose an interdisciplinary approach involving a sophisticated theoretical framework based on mathematical knot theory and Monte Carlo computer simulations, and followed by experimental validation. The computer implementation is based on a novel idea which will greatly reduce computation time as compared to other computational models of unknotting. Relevance to Public Health: Our method will give us the ability to efficiently simulate wild-type topo II on any distribution of DNA knots. Besides being of theoretical interest, such modeling is relevant to public health. Unknotting assays are used in the design of anti-cancer drugs to identify new topo II inhibitors. Our work will be applied to quantifying the unknotting capabilities of the topo II of a given organism with and without the presence of an inhibitor, thus establishing a precise measure of the inhibitor's effectiveness.